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Find three negative consecutive odd integers such that the product of the two smaller integers is 13 less than four times larger imteger

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Explanation:

Let x be the first negative odd integer.

Then the next two negative consecutive odd integers are x-2 and x-4.

The problem states that the product of the two smaller integers is 13 less than four times the larger integer. In equation form, this can be written as:

(x-4)(x-2) = 4(x) - 13

Expanding the left side of the equation:

x^2 - 6x + 8 = 4x - 13

Simplifying:

x^2 - 10x + 21 = 0

Factoring the left side of the equation:

(x-7)(x-3) = 0

Therefore, x = 7 or x = 3.

If x = 7, then the three consecutive odd integers are 5, 3, and 1, which are not negative.

If x = 3, then the three consecutive odd integers are 1, -1, and -3.

Therefore, the three negative consecutive odd integers that satisfy the problem are -3, -1, and 1.

User Klaas Leussink
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